Many of the methods used
in Statistical
Process Control rely on the
data conforming to a normal
distribution. The central limits theorem
is important because it states that even
if the process itself does not conform to
a normal distribution the means
of samples taken from the process will tend
to be normal, the larger the sample the
greater the tendency. Thus we can analyze
sample (subgroup) means in a way that would
not be valid if applied to individual data
values.
Suppose you:
 take a large number of samples from
a population that does not conform to
a normal distribution
 calculate the mean each of those samples
 find the shape of the population distribution
formed by these sample means
You will find that the distribution of
the sample means will resemble a normal
distribution. The larger the the number
of items in each sample, the better the
approximation.
